First let me say this - the reason for performance anxiety might seem like a lack of focus, therefore I recommend breathing and focusing on the current measure which helps to stay focused. But in reality, lack of focus is only a part of this. If think the most important reason why people are afraid, shaking, and having stage fright when it comes time to play in public is because they are not sure of their abilities.
If they are not sure they can do this, then a simple thought like "Oh my God, it's this tricky part coming up next" will mess everything up. So how do you achieve this confidence in your abilities? How do you remain calm when there is so much going on in your piece?
It is memorization. But it's not only knowing which notes to play when without looking at the music. It's much more than that. You have to know the reason why these notes stand in this specific spot of the score.
In other words, you should know how the piece is put together. It's like you should be thinking like a composer who created it. It's the process of deconstruction and deciphering the piece. I find that one of the simplest means to achieve this level is to mark scale degree numbers above each note (if you can't quickly say it aloud when playing). The difficulty is that you should also notice any modulations (change of keys) within the piece and think in scale degrees of that particular key.
Once you do that, memorize your piece in fragments of one, two, four, eight, sixteen measures and so on until you can play it fluently without stopping from the beginning until the end.
Then do transposition exercises playing the piece in various keys starting with no accidentals and progressing through the circle of fifths (also in fragments). Advance to the next key only when you can play in the current one at least three times in a row correctly.
Of course, ability to transpose requires a knowledge of music theory so make sure you brush up on the basics of that field, too.
Memorize your piece and transpose it to 12 different keys (from memory). Then no matter what happens during your public performance you will never be in peril.
By the way, do you want to learn my special powerful techniques which help me to master any piece of organ music up to 10 times faster? If so, download my video Organ Practice Guide.